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Mirrors > Home > MPE Home > Th. List > undir | Structured version Unicode version |
Description: Distributive law for union over intersection. Theorem 29 of [Suppes] p. 27. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
undir |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | undi 3700 |
. 2
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2 | uncom 3603 |
. 2
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3 | uncom 3603 |
. . 3
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4 | uncom 3603 |
. . 3
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5 | 3, 4 | ineq12i 3653 |
. 2
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6 | 1, 2, 5 | 3eqtr4i 2491 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-v 3074 df-un 3436 df-in 3438 |
This theorem is referenced by: undif1 3857 dfif4 3907 dfif5 3908 bwth 19140 |
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